Stationary Pattern and Global Bifurcation for a Predator–Prey Model with Prey-Taxis and General Class of Functional Responses

Yimamu Maimaiti (), Wang Zhang and Ahmadjan Muhammadhaji
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Yimamu Maimaiti: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
Wang Zhang: School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, China
Ahmadjan Muhammadhaji: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China

Mathematics, 2023, vol. 11, issue 22, 1-21

Abstract: This paper will explore a predator–prey model that incorporates prey-taxis and a general functional response in a bounded domain. Firstly, we will examine the stability and pattern formation of both local and nonlocal models. Our main finding is that the inclusion of nonlocal terms enhances linear stability, and the system can generate patterns due to the effects of prey-taxis. Secondly, we consider the nonlinear prey-taxis as the bifurcation parameter in order to analyze the global bifurcation of this model. Specifically, we identify a branch of nonconstant solutions that emerges from the positive constant solution when the prey-tactic sensitivity is repulsive. Finally, we will validate the effectiveness of the theoretical conclusions using numerical simulation methods.

Keywords: prey-taxis; nonlocal competition; numerical simulation; bifurcation; pattern formation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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